Geometric structures of stable output feedback systems
Zhenning Zhang; Huafei Sun; Fengwei Zhong
Kybernetika (2009)
- Volume: 45, Issue: 3, page 387-404
- ISSN: 0023-5954
Access Full Article
top
Abstract
topHow to cite
topZhang, Zhenning, Sun, Huafei, and Zhong, Fengwei. "Geometric structures of stable output feedback systems." Kybernetika 45.3 (2009): 387-404. <http://eudml.org/doc/37668>.
@article{Zhang2009,
abstract = {In this paper, we investigate the geometric structures of the stable time-varying and the stable static output feedback systems. Firstly, we give a parametrization of stabilizing time-varying output feedback gains subject to certain constraints, that is, the subset of stabilizing time-varying output feedback gains is diffeomorphic to the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices satisfying certain algebraic conditions. Further, we show how the Cartesian product satisfying certain algebraic conditions is imbedded into the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices. Then, we give some eigenvalue properties of the stable time-varying output feedback systems. Notice that the stable static output feedback system, which does not depend on the temporal parameter $t$, is just a special case of the stable time-varying output feedback system. Moreover, we use the Riemannian metric, the connections and the curvatures to describe the subset of stabilizing static output feedback gains. At last, we use a static output feedback system to illustrate our conclusions.},
author = {Zhang, Zhenning, Sun, Huafei, Zhong, Fengwei},
journal = {Kybernetika},
keywords = {diffeomorphism; geometric structure; output feedback; immersion; diffeomorphism; geometric structure; output feedback; immersion},
language = {eng},
number = {3},
pages = {387-404},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Geometric structures of stable output feedback systems},
url = {http://eudml.org/doc/37668},
volume = {45},
year = {2009},
}
TY - JOUR
AU - Zhang, Zhenning
AU - Sun, Huafei
AU - Zhong, Fengwei
TI - Geometric structures of stable output feedback systems
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 3
SP - 387
EP - 404
AB - In this paper, we investigate the geometric structures of the stable time-varying and the stable static output feedback systems. Firstly, we give a parametrization of stabilizing time-varying output feedback gains subject to certain constraints, that is, the subset of stabilizing time-varying output feedback gains is diffeomorphic to the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices satisfying certain algebraic conditions. Further, we show how the Cartesian product satisfying certain algebraic conditions is imbedded into the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices. Then, we give some eigenvalue properties of the stable time-varying output feedback systems. Notice that the stable static output feedback system, which does not depend on the temporal parameter $t$, is just a special case of the stable time-varying output feedback system. Moreover, we use the Riemannian metric, the connections and the curvatures to describe the subset of stabilizing static output feedback gains. At last, we use a static output feedback system to illustrate our conclusions.
LA - eng
KW - diffeomorphism; geometric structure; output feedback; immersion; diffeomorphism; geometric structure; output feedback; immersion
UR - http://eudml.org/doc/37668
ER -
References
top- Differential geometry of a parametric family of invertible linear systems-Riemannian metric, dual affine connections, and divergence, Math. Systems Theory 20 (1987), 53–83. Zbl0632.93017MR0901894
- Generalized Inverses, Wiley, New York 1972.
- Global structure of families of multivariable linear systems with an application to identification, Math. Systems Theory 18 (1985), 329–380. MR0818420
- Covariance control theory, Internat. J. Control 46 (1987), 13–32. MR0895691
- Symplectic mechanics and rational functions, Ricerche Automat. 10 (1979), 107–135. MR0614258
- Geometric structures of stable state feedback systems, IEEE Trans. Automat. Control 38 (1993), 1579–1583. MR1242914
- Differential geometric structures of stable state feedback systems with dual connections, Kybernetika 30 (1994), 369–386. MR1303289
- Relations between a parametrization of Stabilizing state feedback gains and eigenvalue locations, Systems Control Lett. 16 (1991), 261–266. MR1102211
- Dualistic Differential geometry of positive definite matrices and its applications to related problems, Linear Algebra Appl. 247 (1996), 31–53. MR1412739
- Robust stabilization for structurally perturbed plants by assigning a Lyapunov equation’s solution, (In Japanese.) Trans. SICE 25 (1989), 682–689.
- Geometric structures of stable time-variant state feedback systems, J. Beijing Institute of Technology 16 (2007), 500–504. MR2375866
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.